Using Lotka's linear age-dependent model of population growth as the focal point, nonlinear systems of differential and integral equations are developed in which age-dependent maternity andmortality moduli evolve in response to the dynamics of the system in the past. These include the models commonly refered to in mathematical demography as the "cohort" model and the "welfare" model. It is shown that for a wide class of these equations, the integral equations can be reduced to a system of differential equations. It has been previously shown by this author that the positive equilibrium of the cohort model bifurcates for a certain value of a parameter to a periodic solution of period near 2MU, where Mu is the mean age of childbearing in the population. Numerical studies by this author have shown that for some maternity functions the bifurcation process is very similar to that of the related first order difference equation, while for other, seemingly more realistic, maternity functions, the bifurcation process is significantly different. The study of the finite dimensional systems of differential equations, for which more powerful analytic tools are available, is expected to provide a much deeper understanding of the basic properties of the age-dependent models than has been possible for the integral equations.